It’s Statistical Modeling Day, so let’s look at one dealing with sexually transmitted diseases. Why this subject? Well, according to New York’s CBS 2, “Study Shows Soaring STD Rates In Many Areas Of New York City: 181 Zip Codes Analyzed And Surge In HIV/AIDS Is Alarming In Some Areas.”
The report said the Department of Health and Mental Hygiene canvassed the city’s neighborhoods for the “concurrence in rates of HIV/AIDS, chlamydia, gonorrhea, syphilis and hepatitis B, as well as two non-sexually-transmitted diseases — hepatitis C and tuberculosis.” TB is transmitted many ways, but “Hep C”, as it is affectionately known, passes all too often through drug use. However, there are too many transmission paths for these diseases for us to consider simply, so we’ll concentrate on STDs.
This are important, too, for as the report indicated:
The study said 33 percent of all the ZIP codes in New York City were in the top quintile citywide for multiple sexually-transmitted diseases during a survey taken in 2010. Among the most severe examples is ZIP code 10474 in Hunts Point, the Bronx, where rates of hepatitis C, chlamydia, gonorrhea and HIV/AIDS all ranked in the top 20 percent of all New York City ZIP codes.
Faring even worse was ZIP code 10457, in the Tremont section of the Bronx, which ranked in the top quintile for all seven diseases surveyed. Forty-three percent of residents in the neighborhood live below the federal poverty line, the report said.
Here’s our model. Suppose capital and lower-case letters represent the two sexes; it doesn’t matter which is which. Suppose A mates with a, B with b, and so forth, with the latter letters not mating with anybody (X,x,Y, and so on become priests, nuns, or New York Times subscribers). Also, an AA (so that we have more than 26 pairs of individuals) might even mate with another AA, etc. Let’s be clear: A does not mate with b, nor c with E. That is, once a letter matches its mate, it sticks to it and never switches.
We have the sexual mating piece, and now need the diseases. Sprinkle them liberally among our “people”, with fractions of HIV/AIDS, chlamydia, gonorrhea, syphilis and hepatitis B equaling that of reality. Maybe, say, 25% of our population have these diseases, let us suppose in equal amounts, and randomly.
This is a model, and therefore like all models only tenuously connected with reality; nevertheless if cautiously approached it can give us hints about reality—as long as we don’t take it too seriously.
Now if A has (say) gonorrhea, then a is likely to get it, too. But A (and a) can trundle off to the doctor and cure it. They might not, and so there is a chance that their offspring catch this disease through pregnancy. However, it’s not a sure thing; and then the offspring will probably seek out treatment (STDs are routinely screened for at pregnancy). HIV is different: it is not curable and can be passed to offspring (but only when capital and lower-case letters mate; if equally cased letters mate there are no offspring, of course).
B and b and C and c and even EE and EE etc. (suppose) have nothing. Since they have matched their letters, it is impossible they should catch anything—unless by the rare chance via drug use or contact with specimens. If, on these unlikely occasions one or both of the pair do contract a disease, they move to the category of A and a above.
Well, that’s it, really; that’s our entire model. You can see how far from reality it is, because if people stuck to the model, then STDs would rapidly die out or become as rare as cases of scurvy. A benefit not to be overlooked is the enormous cost savings of a program (even, yes, a government program, but better originating in the family) which encourages people to emulate the model.
But since I am a realist, and as I have already warned, there is no chance this model will ever hold for the entire population. Notice, though, that it can hold for subgroups of the population, even subgroups as small as “A and a.”
See? Something can be learned from this model after all.